Problem: Solve for $x$ and $y$ using elimination. ${x+3y = 26}$ ${-x+2y = 14}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $5y = 40$ $\dfrac{5y}{{5}} = \dfrac{40}{{5}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {x+3y = 26}\thinspace$ to find $x$ ${x + 3}{(8)}{= 26}$ $x+24 = 26$ $x+24{-24} = 26{-24}$ ${x = 2}$ You can also plug ${y = 8}$ into $\thinspace {-x+2y = 14}\thinspace$ and get the same answer for $x$ : ${-x + 2}{(8)}{= 14}$ ${x = 2}$